There are 10 finalists in a figure skating competition. How many ways can gold, silver, and bronze medals be awarded?

The gold, silver, and bronze medals can be awarded in ????
ways.

It will take 35 years to double the population

Percentages are just fractions with a denominator of 100. To show that a number is a percentage, we place the percent sign (%) next to it. For instance, if you properly answered 68 out of 100 questions on a test, you would have received a 68% grade (68/100).

According to the given information

Let [tex]P(0)[/tex] be initial population

and K be the growth rate

Then Population of the country after t years

[tex]P = P(0)e^{Kt}[/tex]

Let x be the present population

2x will be the double of present population

And we know

The growth rate K = 0.02%

So

The value of t could be determined as follows

[tex]xe^{0.02t}=2x[/tex]

[tex]e^{0.02}=2[/tex]

[tex]0.02t=ln(2)[/tex]

Multiply both sides by 1000

0.02t × 1000 = ln(2) × 1000

Refine

20t = ln(2) × 1000

Divide both sides by 20

[tex]\frac{20t}{20}=\frac{ln(2).1000}{20}[/tex]

t = [tex]ln(2).500[/tex]

t = 0.693×50

t = 34.65 years

t = 35 years

It will take 35 years to double the population

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The price of the watch before the discount is calculated to be £24.44.

As the total price of the watch and a pair of trainers is £53. 55 and the price of the trainer before the discount was £38, we first calculate the price of the trainers after the discount as follows;

discount on a pair of trainers = 15/100 × 38 =  £5.7

cost of trainers after discount =  £38 - 5.7 =  £32.3

Now the price of the watch after the discount can be calculated by subtraction as follows;

price of watch after discount = total price - price of trainers after discount

price of watch after discount =  £53. 55 - £32.3

price of watch after discount = £21.25

Now the price of the watch before the discount can be calculated as follows;

price of watch before discount = £21.25 × 15/100

price of watch before discount = £21.25 + £3.1875

price of watch before discount = £24.44

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The area of a rectangle is 42 quare millimeter. The length is 7 millimeter. 28 millimeters is the perimeter of the rectangle.

Perimeter = 2 × (Length + Width)

Perimeter = 2 × (7 + 6)

Perimeter = 28 millimeters

To calculate the perimeter of a rectangle, we need to multiply the length and the width of the rectangle, and then multiply that value by 2. In this case, the length is 7 millimeters, and the area is 42 square millimeters. To calculate the width, we can divide the area by the length, which is 42 divided by 7, which is equal to 6. So the width is 6 millimeters. Now we can calculate the perimeter using the formula: Perimeter = 2 × (Length + Width). Plugging in the values, we get: Perimeter = 2 × (7 + 6) = 28 millimeters.

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Answer:

65 mph;  35 mph

Step-by-step explanation:

let x = rate of car 1

x-30 = rate of car 2

distance = rate x time

6x = 600 - 6(x-30)

6x = 600 - 6x + 180

6x = 780 - 6x

12x = 780

x = 780/12 = 65 mph

x - 30 = 65 - 30 = 35 mph

The solution to the system of linear equations 3y = x + 21 and y + 2/3x = 10

is (x, y) = (3, 8)

A system of linear equations is a collection of at least two linear equations.

From the question, we have the following parameters that can be used in our computation:

In this case, the system of equations is given as

3y = x + 21

y + 2/3x = 10

Next, we plot the graph of the system of equations

In this case, the point of intersection of the equations represent the solution to the system

From the graph, the lines intersect at (3, 8)

Hence, the solution is (3, 8)

In (a), we have

The lines intersect at (3, 8)

This means that

(x, y) = (3, 8)

So, we have

3 * 8 = 3 + 21 = 24

y + 2/3 * 3 = 10

The above equations are true

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The sign change of the expression ax + b = cx + d in the conditions are solved to be

a. 0 < b < d and a < c

b. d < b < 0 and a < c

The given expression is

ax + b = cx + d

comparing the conditions

a. 0 < b < d and a < c

here b is non negative number and less than d a is also less than c. hence

ax + b = cx + d

ax - cx = d - b

ax - cx will be negative

d - b will be positive

this will lead to a negative solution since positive divided by negative  give negative

b. d < b < 0 and a < c

ax + b = cx + d

ax - cx = d - b

d - b = negative

ax - cx = negative

negative dividing negative is positive hence a positive solution

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Answer:

it would be quadrant |||

so answer choice C

Step-by-step explanation:

Answer:

b) arithmetic

Step-by-step explanation:

Knowledge Needed

c and d are not valid sequence types.

Geometric Sequences are when the values of terms are found by multiplying the previous term's value by the same number.

Example:

1, 2, 4, 8, 16

x2

2, 6, 18, 54, 162

x3

20, 10, 5, 2.5, 1.25

x0.5

Arithmetic Sequences are when the values of terms are found by adding the previous term's value by the same number.

Example:

5, 6, 7, 8

+1

7, 19, 31, 43

+12

9, 6, 3, 0

-3

Question

Examine the sequence. From viewing the first 2 terms, we know that it can either be a geometric sequence that multiplies by 11/3 every time the term increases or an arithmetic sequence that adds 8 every time the term increases.

Looking at the 2nd and 3rd term, we know it is an arithmetic sequence because 19 is not equal to 11 times 11/3.

In the first circle, the measure of angle ABC is 24°

In the second circle, the measure of angle ABC is 20°

From the question, we are to determine the measure of angle ABC

In the first diagram,

The measure of the arc is 48°

From one of the circle theorems, we have that

The angle subtended by an arc in a circle is twice the angle subtended at the circumference.

Then, we can write that

2 × ∠ ABC = 48°

∠ ABC = 48°/2

∠ ABC = 24°

Question 5

Using the same theorem,

The angle subtended by an arc at the center of the circle is twice the angle subtended at the circle

∠ ABC = 1/2 × 40°

∠ ABC = 20°
Hence, the measure of the angle is 20°

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The real and imaginary parts of the three complex numbers are:

In this question we find three case of complex numbers, that is, numbers of the form z = a + i b, where a, b are real coefficients and i = √(- 1). The coefficient a corresponds to the real part of the complex number and the coefficient b is its imaginary part. Now we proceed to analyze each of the three cases:

Case 1: - 7

The number - 7 is equivalent to - 7 + i 0, where - 7 is the real part and 0 is the imaginary part.

Case 2: 5 - √(- 24)

First, we rewrite the entire expression in standard form:

5 - √(- 24)

5 - √[(- 1) · 24]

5 - √(- 1) · √24

5 - i √24

5 - i 2√6

The real part is 5 and the imaginary part is 2√6.

Case 3: (6 - i) · (6 + i)

We expand and simplify the resulting expression:

(6 - i) · (6 + i)

6 · (6 - i) + i · (6 - i)

36 - i 6 + i 6 - i²

(36 - i²)

36 + 1

37

37 + i 0

The real part is 37 and the imaginary part is 0.

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Answer:

The real and imaginary parts of the three complex numbers are:Real part: - 7, Imaginary part: 0Real part: 5, Imaginary part: 2√6Real part: 37, Imaginary part: 0How to determine the real and imaginary component of a complex number.In this question we find three case of complex numbers, that is, numbers of the form z = a + i b, where a, b are real coefficients and i = √(- 1). The coefficient a corresponds to the real part of the complex number and the coefficient b is its imaginary part. Now we proceed to analyze each of the three cases:Case 1: - 7The number - 7 is equivalent to - 7 + i 0, where - 7 is the real part and 0 is the imaginary part.Case 2: 5 - √(- 24)First, we rewrite the entire expression in standard form:5 - √(- 24)5 - √[(- 1) · 24]5 - √(- 1) · √245 - i √245 - i 2√6The real part is 5 and the imaginary part is 2√6.Case 3: (6 - i) · (6 + i)We expand and simplify the resulting expression:(6 - i) · (6 + i)6 · (6 - i) + i · (6 - i)36 - i 6 + i 6 - i²(36 - i²) 36 + 137 37 + i 0The real part is 37 and the imaginary part is 0.

Step-by-step explanation: hope this helps0^0

Answer:

Step-by-step explanation:

To find the value of z such that 0.12 of the area lies to the right of z, we need to know the distribution of the data and the total area under the curve. If the data follows a normal distribution, the area under the curve is always 1, and 0.12 of the area corresponds to a z-value of approximately 0.84.

We can use a standard normal table or a calculator to find the exact value of z. For example, using a standard normal table, we can find that the z-value corresponding to an area of 0.12 to the right of z is 0.8416.

Therefore, the value of z such that 0.12 of the area lies to the right of z is approximately 0.84.

Answer:

68cm

Step-by-step explanation:

Because the scale factor is 2, which means the drawing is 2 times smaller than the actual airplane, multiply 34, the length of the wings tip to tip in the drawing by 2.

34 x 2 = 68

Answer: 68 meters

(Hope I'm correct, but read the explanation to make sure)

Step-by-step explanation:

Let's start with what we know. We know that the scale factor is 2, so in our model, from tip to tip, it is 34 cm. However, since the scale factor is 2:
34 * 2 = 68 meters

Let's say Chloe spent X

Then Amy spent 60% more so Amy spent

X+60% of X =X + 0.6X =1.6X

Becky spent 15% of what Chloe spent so amount spent by Becky =15% of X = .15X

Now, in total, they spent 0.15X+ X + 1.6X =2.75X which is given as £55

So , X=55/2.75 = 20

Amount spent by Amy = 1.6X = 1.6 *20 =£32

Answer: 18

Step-by-step explanation:

there you go <3

Answer:

12

Step-by-step explanation:

1 -----> 3

?------>36

By make Cross

36*1/3 =12

Answer: $0.08

Step-by-step explanation:

First, let's find last week's price

Take 35.40 divided by 12 = $2.95 per gallon

Next, find this week's price

Take 25.83 divided by 9 = $2.87 per gallon

Then take 2.95 - 2.87 = $0.08

Answer:

Step-by-step explanation:

[tex]log_{10}(2000xy)-(log_{10}x})(log_{10}y)=4\\\\log_{10}(2000(xy))-log_{10}(xy)=4\\\\log_{10}(2000)+log_{10}(xy)-log_{10}(xy)=4\\\\log_{10}(2(1000)=4\\\\log_{10}2+log_{10}(1000)=4\\\\log_{10}2+log_{10}(10^3)=4\\\\log_{10}2+3log_{10}(10)=4\\\\log_{10}2\approx0.3\\\\Hence,\\\\log_{10}2+3\neq 4[/tex]

[tex]log_{10}(2yz)-(log_{10}y)(log_{10}z)=1\\\\log_{10}(2(yz))-log_{10}(yz)=1\\\\log_{10}2+log_{10}(yz)-log_{10}(yz)=1\\\\log_{10}2\neq 1[/tex]

[tex]log_{10}(zx)-(log_{10}z)(log_{10}x)=0\\\\log_{10}(zx)-log_{10}(zx)=0\\\\0\equiv0[/tex]

Answer: 6000 students

Step-by-step explanation:

First, we find the 40% that the university accept

40% = 0.4

Take 30000 times 0.4 = 12000 students got accept

Now we find the 50%

50% = 0.5

Take 12000 times 0.5 = 6000 students

6000 students would actually enroll

The function has no vertical asymptotes and the horizontal asymptotes of the function is y=0.

In the given question,

Consider the following function.

f(x) = e^{−x^2}

We have to find the vertical asymptote(s), x = Find the horizontal asymptote(s) or y = .

As we know that, a vertical asymptote is a line that runs vertically and guides the graph of the function but does not actually exist on it. Due to its position at an x-value that is outside of function's domain, it is difficult for the curve to ever pass it.

The function f(x) = e^{−x^2} has no undefined points. So the function has no vertical asymptotes.

The limit of the function at x→±∞ is calculated as follows:

[tex]\lim_{x\rightarrow \pm\infty }[/tex]f(x) = [tex]\lim_{x\rightarrow \pm\infty }[/tex]e^{−x^2}

[tex]\lim_{x\rightarrow \pm\infty }[/tex]f(x) = 0

So the horizontal asymptotes of the function is y=0.

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The right question is:

Consider the following function. (If an answer does not exist, enter DNE.) f(x) = e^{−x^2}. Find the vertical asymptote(s). (Enter your answers as a comma-separated list.) x = Find the horizontal asymptote(s). (Enter your answers as a comma-separated list.)

y =

Yes, this statement is correct because in quadrilaterals if two lines are parallel, then the other two sides have to be equal in length.

Triangles that are equal in all ways and interchangeable are typically described as being congruent.

A triangle with equal legs, such as an isosceles triangle, may have equal legs that are also equal to the two equal legs of another triangle with equal legs, but if the included angle is different, the triangles are not congruent.

Two sides are simply equal if their lengths are the same.

When it comes to parallelograms, both opposite side pairs are equal and parallel.

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The sum of two number is 92. Their difference i 20Let x and y represent the 2 number. Let x=the lager value and smaller valuex = 92 + 20 = 11,y = 92 - 20 = 72

Let x = the larger value and y = the smaller value.

We know that the sum of x and y is 92, so

x + y = 92

We also know that the difference between x and y is 20, so

x - y = 20

Add the two equations to get

2x = 112

Divide by 2 to get

x = 112

Substitute x = 112 into the first equation to get

112 + y = 92

Subtract 112 from both sides to get

y = 72

Therefore, the two numbers are x = 112 and y = 72.

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The slope of the roof is 0.25

What is a slope ?

A line's slope is how steeply it slopes from LEFT to RIGHT. The slope of a line is determined by dividing its rise, or vertical change, by its run, or horizontal change. No matter which two locations on the line you choose, the slope of a line is always constant (it never varies).

The ratio of the increase in elevation between two points to the run in elevation between those same two points is referred to as the slope.

The slope-intercept form of an equation is used whenever the equation of a line is expressed in the form y = mx + b. M represents the line's slope. And b is the value of b at the y-intercept (0, b).

To find slope

= 6.25 / 25

= 0.25

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Answer: Median is 12, mode is 5, mean is 13.71

Step-by-step explanation:

Answer:

The median is 18

The mode is 5

The mean is 13

Step-by-step explanation:

The tree will be 75 feet tall when it will be fully grown.

The total tree height is the distance between the tree's base and its highest point on the ground. A yardstick provides a quick and relatively accurate way to gauge the height of a tree.

If the tree is currently 60 feet tall and is approximately 80% of its full height, we can assume that the tree will be 100% of its full height when it is fully grown. To determine the full height of the tree, we can use the proportion:

60 feet / 80% = X feet / 100%

We can then cross-multiply to solve for X:

X = (60 feet * 100%) / 80%

= 75 feet

So, when the tree is fully grown, it will be approximately 75 feet tall.

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The value of x is in the solution set of the inequality 9(2x + 1) < 9x – 18 is -4.

Inequality is defined as relationship between non-equal numbers or expressions. The solution set of an inequality is the set of values that satisfies the given inequality.

To determine the solution set of the given inequality, isolate the variable to one side and simplify.

9(2x + 1) < 9x - 18

18x + 9 < 9x - 18

18x - 9x < -18 - 9

9x < -27

x < -3

x = (-∞, -3)

Hence, the solution set of the given inequality is the set of numbers less than -3. Among the given choices, only -4 is less than -3. Therefore, the value of x is -4.

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Answer: -4

Step-by-step explanation: edge2020

Evelyn basis is the adjusted market value of the property and the basis would have been to Evelyn as profit

We should know that adjusted basis is the value of a property after deducting all expenses and taxes from the property.

The Adjusted basis of the property was $12,000

It was given to Sharon at fair value of $80,000

After  death of Sharon, the property was worth $85,000

Based on these figures, the basis is a gain of $(85000-80000) to to Evelyn

In conclusion, Evelyn has gained the sum of $(85000-12000)=$73000

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Distance covered by Yochanan by walking = 5 km

Distance covered by Yochanan by bus = 30 km

Given the values in the question,

The average speed of Yochanan when he walked to the bus stop from home = 5 km/h

The average speed of the bus till Yochanan reached his school = was 60 km/h

The total distance between his school from home = is 35 km

Time is taken by the entire trip = 1.5 hours

Relation between Distance, Time, and speed,

⇒ Average Speed = [tex]\frac{Distance}{Time}[/tex]

Let us consider that Yochanan walked = a km

The bus travelled = 35 - a

We know that the total time is constant so,

⇒ T = T1 + T2

⇒ 1.5 = [tex]\frac{x}{5} + \frac{35-a}{60}[/tex]

Solving for a,

⇒ 1.5 = [tex]\frac{12a + 35 - a}{60}[/tex]

⇒ 11 a + 35 = 90

⇒ 11 a + 55

⇒ a = 5

The distance covered by Yochanan by walking = a = 5 km

Distance covered by bus = 35 - a

= 35 - 5

= 30 km

Therefore, the distance covered by Yochanan by walking = is 5 km, distance covered by Yochanan by bus = is 30 km

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Yochanan walked from home to the bus stop at an average speed of 5 km/h he immediately got on his school bus and traveled at an average speed of 60 km/h until he got to school. the total distance from his home to school is 35 kilometers, and the entire trip took 1.5 hours. how many kilometers did Yochanan cover by walking, and how many kilometers did he cover by traveling on the bus? Yochanan walked kilometers and traveled kilometers on the bus.

The present age of Jiya whose mother 12 year more than twice her age., is sixteen years and her mother present age is fourty-four years.

We have, Jiya's mother is 12 year more than twice of her age. Let "x years" and "y years" be the present age of Jiya and her mother respectively.

According to problem, 12 + 2x = y --(1)

After 8 years, her mother age = 20 years less then three times of her age.

After 8 years, age of Jiya = (x+8) years.

i.e y + 8 = 3( x+8) - 20 --(2)

we have to calculate the present ages of both. Simplify the equation (2),

y + 8 = 3x + 24 - 20

=> y + 8 = 3x + 4 => y = 3x -4 --(3)

eqution (1) and (3) represent the linear equations so, we solve these linear equations by substitution,

plugging the value of y from( 1) to (3),

12 + 2x = 3x -4

=> 3x - 2x = 12+4

=> x = 16 then y = 12 + 2×16 = 44

Hence, Jiya's age is 16 years and her mother is about 44 years.

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